Social media systems typically display conversations among already familiar contributors, which can be predictable and one-sided. In civic discourse, this design narrows discussion, reinforces divides, and distorts the perception of public opinion. To encourage cross-community engagement, we present CrossWeave, an AI-powered bridging system that augments the standard social media feed. As the user reads a post, CrossWeave surfaces diverse relevant posts from other threads in a side pane and highlights the connections. Users are invited to venture out of their echo chamber, explore a broader range of views and arguments, and ``click across'' to engage with their authors. When they do, CrossWeave facilitates constructive posting, not only by showcasing relevant past content but also by simulating possible reactions as the user drafts a post.

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